Question 127
Let $x_1,x_2,\ldots,x_{2008}$ be real numbers satisfying $|x_1|=999$ and
$$
|x_n|=|x_{n-1}+1|\qquad(2\le n\le 2008).
$$
Determine the smallest possible value of $x_1+x_2+\cdots+x_{2008}$.
$$
|x_n|=|x_{n-1}+1|\qquad(2\le n\le 2008).
$$
Determine the smallest possible value of $x_1+x_2+\cdots+x_{2008}$.